In a cyclic quadrilateral ABCD, if (∠B – ∠D) = 60o , show that the smaller of the two is 60o

ANSWER

It is given that ABCD is a cyclic quadrilateral  

(∠B−∠D)=60  

o

(1)

(∠B+∠D)=180  

o

(2)

By adding both the equations

∠B−∠D+∠B−∠D=60  

o

+180  

o

So we get  

2∠B=240  

o

By division

∠B=120  

o

By substituting equation it in equation (1)

(∠B−∠D)=60  

o

120  

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−∠D=60  

o

On further calculation  

∠D=120  

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−60  

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by subtraction  

∠D=60  

o

Therefore, the smaller of the two angles ∠D=60  

o

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Step-by-step explanation:

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step-by-step explanation: